PreprintSecond \(p\)descents on elliptic curvesBrendan CreutzAbstractLet \(p\) be a prime and let \(C\) be a genus one curve over a number field \(k\) representing an element of order dividing \(p\) in the ShafarevichTate group of its Jacobian. We describe an algorithm which computes the set of \(D\) in the ShafarevichTate group such that \(pD = C\) and obtains explicit models for these \(D\) as curves in projective space. This leads to a practical algorithm for performing explicit 9descents on elliptic curves over \(\mathbb{Q}\) Keywords: elliptic curves, descent, ShafarevichTate group.AMS Subject Classification: Primary 11G05; secondary 11Y50.
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